I've got a cd called The Police Live. It's from a 1983 show.
The Police were a revolutionary band. The drumming is unique. The rhythm guitar playing added new chords to the rock vocabulary. They completely turned the idea of a three-piece band (formerly known as a power trio) into something else.
As far as classic songs, I think you have to add Message in a Bottle, Don't Stand So Close to Me", and "De Do Do Do, De Da Da Da".
I have an earlier live recording (a bootleg). They really killed in their early days.
Stewart Copeland and I both went to the University of California, Berkeley at the same time, but he did not take any music classes there, so unfortunately I never met him.
I'd put him in the hall of fame for drummers just for his snare drum sound.